In this question, we have to check that if the pairs of triangles are similar.
Let's evaluate both the parts.
1) Part 1:
In this part, we have only two angles given. Therefore, we can only apply the AA postulate. It states that two triangles are similar if they have two corresponding angles equivalent. Also, the sum of all the angles in 180.
if we see the first triangle, the missing angle can be found using (180 - 70 -40 = 70). Hence, the angles are 70, 70 and 40
For the second triangle, the missing angle is (180 - 70 - 70 = 40).
Therefore, both the triangles have equivalent corresponding angles. Therefore, according to AA, both the triangles are similar.
2) part2:
In this part, we have only two sides given. Therefore, we can only apply the SSS postulate. It states that two triangles are congruent if all the sides of the triangle are congruent to the corresponding sides of other triangle.
For that, check the ratio of all the corresponding sides. If they are the same, then the triangle is similar.
Base1/ base2 = 10/6 = 5/3
hypotenuse1/ hypotenuse2 = 15/9 = 5/3
If two sides have the same ratios, the ratio of the third side would also be the same. Therefore, according to SSS, both the triangles are similar.